SUVAT equations calculator
SUVAT problems always give you three quantities and ask for one or two more. Enter your three values, leave the other two empty and read off the solution with its working.
How this calculator works
The five SUVAT letters stand for displacement, initial velocity, final velocity, acceleration and time. They describe motion in a straight line where the acceleration stays constant, such as a dropped ball, a braking car or a sprinter off the blocks.
The trick with these problems is choosing the equation that contains your three knowns and one unknown. The calculator does that for you for all ten possible combinations, then works out the second unknown from the first. Pick a positive direction and stick to it: a ball thrown upward at 15 m/s has u = +15 and a = -9.8.
The formula behind it
- v = u + at
- s = ut + ½at²
- s = ½(u + v)t
- v² = u² + 2as
- s = vt - ½at²
A worked example
A stone is dropped from rest, so u = 0, a = 9.8 and t = 3 s. Then v = 0 + 9.8 × 3 = 29.4 m/s and s = 0 + ½ × 9.8 × 9 = 44.1 m.
Questions people ask
What if the answer has two possible values?
Using v² = u² + 2as gives a positive and a negative root. The calculator shows the one that goes with positive time and tells you a second solution exists.
Can acceleration be negative?
Yes. A negative value means the object is slowing down relative to your chosen positive direction.
What if I know four values?
Then one is redundant. Leave one blank and let the calculator check it: if your fourth value differs from the result, something in the question or your data does not fit.
Does SUVAT work with air resistance?
Only if the acceleration is constant. Air resistance changes with speed, so for a falling feather or a skydiver the equations are an approximation at best.